Question

a machine at a bakery is pouring out flour. the graph shows the amount of flour (in grams) in the machine versus time (in minutes). (a) choose the statement that best describes how the time and amount of flour are related. then fill in the blank. as time increases, the amount of flour in the machine decreases. at what rate is the amount of flour decreasing? \boxed{} grams per minute as time increases, the amount of flour in the machine increases. at what rate is the amount of flour increasing? \boxed{} grams per minute (b) what is the amount of flour in the machine at 0 minutes? \boxed{} grams

Explanation:

Step1: Analyze the graph trend

The graph shows a line with a negative slope (going down from left to right), so as time (x - axis) increases, the amount of flour (y - axis) decreases. So we choose the first statement: "As time increases, the amount of flour in the machine decreases."

Step2: Find two points on the line

From the graph, we can identify two points. Let's assume the points are \((0, 630)\) and \((7, 0)\) (since at \(x = 0\) (0 minutes), \(y = 630\) grams and at \(x=7\) minutes, \(y = 0\) grams).

Step3: Calculate the rate of decrease

The rate of change (slope) is given by \(\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(y_1 = 630\), \(y_2=0\), \(x_1 = 0\), \(x_2 = 7\). So the slope is \(\frac{0 - 630}{7-0}=\frac{- 630}{7}=- 90\). The negative sign indicates a decrease, so the rate of decrease is \(90\) grams per minute.

Step4: Find the amount at 0 minutes

From the graph, when \(x = 0\) (time = 0 minutes), the \(y\) - value (amount of flour) is \(630\) grams.

Answer:

s:
(a) Statement: As time increases, the amount of flour in the machine decreases. Rate of decrease: \(90\) grams per minute.
(b) Amount at 0 minutes: \(630\) grams.

(For part (a) first blank: "As time increases, the amount of flour in the machine decreases."; second blank: \(90\); For part (b): \(630\))